Cake:
Interest does not mess up your score; late payments do. If you were to make the minimum payment every time, you would rack up the interest and maybe need decades to pay off a balance, but your score would be great because you did not have late payments.

This is a simplistic view of the process as there are many factors that go in to calculating your scores, but being charged interest on an outstanding balance isn't one of them (unless the interest really drives up your total balance due).

JenWales:
Yes and no. Always pay your card in full to avoid interest, but interest itself won't hurt your credit. If, however, you owe more than 30% of your credit line, your scores will take a hit, then again at 50% and so on. It's best for your FICO scores to never carry a balance higher than 9% (and oddly it is better score-wise to carry a small balance than to owe nothing at all.

Q The First Timelord:
no. all credit cards which carry a balance tend to charge you interest for that balance as a normal part of operations. There's nothing that goes on your credit record other than you paid your monthly payment due on time.

Re Vera:
It still surprises me that people are this ignorant…

Interest is the cost of you borrowing money, be it on a credit card or a car loan or a home loan. The only way it will hurt your credit history is if you fail to pay your bill on time.

Barry A:
If you are paying interest, it means that your payment was late.
One payment may not be reported, but if you make a habit of it, then you will have some problems with the score.

MadMan:
No. Interest is charged if you did not pay the full amount off before the due date.